On Tests of the Conditional Relationship between Beta and Returns

The Pettengill et al (1995) test of the conditional relationship between beta and returns has recently become widely used. This paper shows that there is a large bias in that test. The test is almost guaranteed to be satisfied, regardless of the model that generates expected returns. In particular, even if the CAPM is not true and expected returns and beta are unrelated, the test will detect statistically significant results of the size that they report in line with their hypothesis. The reason for the bias is that the ex post selection criterion used to partition data automatically generates coefficient values that the test interprets as being evidence in favour of the CAPM